arX

iv:1

303.

2260

v1 [

cond

-mat

.mes

-hal

l] 9

Mar

201

3

Spiral graphone and one sided fluorographene nano-ribbons

M. Neek-Amal1, J. Beheshtian2, F. Shayeganfar3, S. K. Singh1, J. H. Los4 and F. M. Peeters1Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium.

2 Department of Physics, Shahid Rajaee teacher Training University, Lavizan, Tehran 16785-136, Iran.3 Departement de genie physique et Regroupement quebecois sur les materiaux de pointe (RQMP),

Ecole Polytechnique de Montreal, C.P. , succ. Centre-Ville, Montreal, Que., Canada H3C 3A7.4 Institute of Physical Chemistry and Center for Computational Sciences,

Johannes Gutenberg University Mainz, Staudinger Weg 9, D-55128 Mainz, Germany(Dated: March 7, 2021)

The instability of a free-standing one sided hydrogenated/fluorinated graphene nano-ribbon, i.e.graphone/fluorographene, is studied using ab-initio, semiempirical and large scale molecular dy-namics simulations. Free standing semi-infinite arm-chair like hydrogenated/fluorinated graphene(AC-GO/AC-GF) and boat like hydrogenated/fluorinated graphene (B-GO/B-GF) (nano-ribbonswhich are periodic along the zig-zag direction) are unstable and spontaneously transform into spiralstructures. We find that rolled, spiral B-GO and B-GF are energetically more favorable than spiralAC-GO and AC-GF which is opposite to the double sided flat hydrogenated/fluorinated graphene,i.e. graphane/fluorographene. We found that the packed, spiral structures exhibit unexpected local-ized HOMO-LUMO at the edges with increasing energy gap during rolling. These rolled hydrocarbonstructures are stable beyond room temperature up to at least T=1000K.

I. INTRODUCTION

The discovery of graphene [1] has been a driving forcefor the scientific community to synthesize and to char-acterize new materials with similar morphologies due totheir unique properties [2–5]. Fully double sided hydro-genated graphene (GE), i.e. graphane (GA), and doublesided fluorographene are quasi two-dimensional latticesof carbon (C) atoms ordered into a buckled honey-

comb sublattice, where each carbon atom is covalentlybonded to hydrogen (H) or fluor (F), respectively, in analternating, chair-like arrangement [6, 7]. The chemisorp-tion of hydrogen and fluor atoms results in an importantreconstruction of the chemical bonds and angles of theunderlying honeycomb lattice [8]. This transition fromsp2 to sp3 hybridization turns the graphitic C-C bondsinto single bonds by the formation of additional single C-H and C-F bonds, which change locally the planar shapeof graphene into an out of plane, angstrom scale buckledgeometry [9].

Experimentally, it has been shown that GA can be ob-tained reversibly starting from a pure GE layer in thepresence of atomic hydrogen [10]. It has become an in-teresting material due to its potential applications in na-noelectronics [11]. On the other hand, the experimentallyobtained single-layer fluorographene exhibits a strong in-sulating behavior with a room temperature resistancelarger than 1 TΩ, and a high temperature stability upto 400 oC [7].

Both in experiments [10] and in ab-initio calculations,flat single-sided hydrogenated graphene, graphone (GO),was found to be unstable [9, 12–17] which was alsodemonstrated by phonon band structure calculations.Supporting graphene on a substrate and hydrogenatingwas demonstrated to produce GO in a recent experi-ment [18]. Ab-initio calculations showed that arm-chair(AC)-GA is more stable than boat like (B)-GA while

a) B-GO

b) AC-GO

FIG. 1: (Color online) Side views of a small portion of simu-lated graphones which were relaxed at T=10K using molec-ular dynamics simulation. Arm-chair graphone (a) and boat-like graphone (b).

B-GO was found to be more stable than AC-GO [19].Ab-initio calculations also showed that GO exhibits mag-netism due to the localized electrons on the carbon atomswithout hydrogens, in contrast to nonmagnetic grapheneand graphane [20, 21].

By using both ab-initio calculation and elasticity the-ory, Kudin et al found that while linear elasticity theorycan be used for studying the stiffness and flexural rigiditymoduli of carbon and boron-nitride nanoshells, one-sidedfluorinated carbon ribbons exhibit a strong tendency toshell formation resulting into very small diameter tubeswith (4,4) and (3,3) indexes and properties that devi-ate from linear elasticity theory [22]. Such a strong ten-dency to bending is also observed for Si and bilayer SiGenanofilms, due to reconstructions in the surface layer [23]associated with dimer formation. Although the possibledeformation of the edge of graphene (see [24] and refer-ences therein) and the synthesis of carbon nanotubes viaone-sided hydrogenation or fluorination of supported car-bon films have been investigated theoretically [25], the

2

geometrical structure of long (referring to the distancebetween the free edges) nano-ribbons of graphone andtheir corresponding stability and electronic properties atroom temperature have not been studied so far. Here weshow that such long nano-ribbons of GO/GF do not formcarbon nanotubes, as in the case of relatively short sam-ples with specific sizes [25], but, instead, spontaneouslyform rolled, spiral structures with interesting localizationof frontier molecular orbitals. The one-sided absorptionand corresponding sp3 hybridization is the main drivingforce for this transformation, and the final spiral struc-ture is significantly more stable than the correspondingflat structures. We used the three mentioned methodsto investigate various electronic and geometrical proper-ties of these new spiral structures, which we named spiralgraphone (fluorinated graphene)’.There have been several recent experimental and the-

oretical studies related to the formation of carbon nan-otubes using a graphene sheet and inverse processing [26–28]. Many experimental evidences point towards thepossibility of the production of the here proposed spi-ral carbon nanostructures. In a recent review paper, Vi-latela and Eder [29] reviewed related experimental stud-ies, compared the potentials and characteristics of nanocarbon composites (such as various rolled sheets) anddiscussed key challenges for the use of the new carbonnanostructures. Furthermore, similar rolled structuresfor Ni3Si2O5(OH)4 were synthesized and analyzed usingX-ray diffraction (XRD) and transmission electron mi-croscopy (TEM) [30]. Shen et al [31] reported recentlythe synthesis of self-assembled kinked In2O3 nanospi-rals and multikinked nanowires using a tube-in-tube laserablation chemical vapor deposition (CVD) method withgold nanoparticles as the catalysts.Apart from being more stable than the flat structures,

we also show that spiral B-GO and B-GF are more sta-ble than spiral AC-GO and AC-GF, respectively. Thespiral structures are closely packed and stable even at1000 K and are candidates for a new class of carbonnano-structures. Since the deformations for the GFsand the GOs are very similar we will report here mainlythe results for the GOs. After rolling, the highest oc-cupied orbital (HOMO) and the lowest unoccupied or-bital (LUMO) are separated and appear to be localizedat opposite (free) ends, making these two ends chemicallymore active [32], while before and during rolling they arelocalized at both ends simultaneously. We found that therolling process makes the systems strongly polarized andmore insulating.

II. METHODS AND MODELS

We performed ab-initio calculations using GAUSSIAN(G09) [33] which is an electronic structure package thatuses a basis set of Gaussian type of orbitals. In the ab-inito calculations for the exchange and correlation (XC)functional, the hybrid functional B3LYP is adopted in

G09. The self consistency loop was iterated untill thechange in the total energy is less than 10−7 eV, and thegeometries were considered relaxed once the force on eachatom is less than 50meV/A. Using the 6-31G* basis set inG09, we expect that our calculation is capable to providea reliable description of the electronic properties of thedifferent systems. In the case of AC-GO the A-sublatticesites of GE were covered with hydrogens, while the B-GOmodel was obtained by hydrogenating all carbon atomsinvolved in horizontal C-C bonds along the AC direction.Hence the number of carbon atoms is twice as large asthe number of hydrogen atoms. The simulated samples(using the DFT method) have typically more than 500atoms.For the larger samples, we performed semi-empirical

calculations (PM6 level of calculation in G09) as well asclassical molecular dynamics simulations (MD) using theLAMMPS package [34].For the classical MD simulations, the modified second

generation of Brenner’s bond-order potential, i.e. Adap-tive Intermolecular Reactive Bond Order (AIREBO) [35]and the ReaxFF [36] potentials were employed to simu-late the GOs and GFs, respectively. These simulationswere performed using periodic boundary conditions alongthe lateral side (perpendicular to the rolling direction) inthe canonical NVT ensemble with a Nose-Hoover ther-mostat for temperature control and a time step of 0.1 fs.The simulation box size along the rolling direction wastaken equal to twice the system size (in its flat geometry)in that direction.AIREBO consists of two parts, namely the reactive

bond order potential (REBO [37]) for the short range in-teractions (<2 A), but with a modified, four body, bondorder contribution for the torsion in various hydrocarbonconfigurations, and the van der Waals (vdW) term forlong range interactions within distances 2 A < r < 10 Awhich is similar to the standard Lennard Jones potential,but with an environment dependent (adaptive) suppres-sion of the (too) strong 1/r12 repulsion. Its total energyreads:

EAIREBO = E′

REBO + EvdW , (1)

where the prime in E′

REBOis added to indicate the mod-

ification in the torsion term. In our MD simulationswe checked the effect of the vdW term (by turning iton/off) to insure that when GO is rolled up the vdW termdoes not prevent possible bonding between two close edgeatoms. The simulations where we included the vdW termare labeled with the symbol ∗. We found that includingthe vdW term lowers the energy of spiral GO* by only0.04 eV/atom with respect to GO.In ReaxFF (for simulating B/AC-GFs), the atomic in-

teractions are described by a reactive force field poten-tial [36]. ReaxFF is a general bond-order dependent po-tential that provides an accurate description of the bondbreaking and bond formation. Recent simulations ona number of hydrocarbon-oxygen systems showed that

3

(a)

(b)

FIG. 2: (Color online) (a) The spiral B-GO using DFT cal-culations for 504 atoms. (b) The spiral B-GO using semiem-pirical calculations (PM6) for 1320 atoms.

ReaxFF reliably provides energies, transition states, re-action pathways and reactivity in reasonable agreementwith ab-initio calculations and experiments.For our MD simulations, our rectangular GO nano-

ribbons contained different numbers of carbon atoms,namely NC = 4800 and 5760. For the GFs we tookNC = 5600. For the semi-empirical calculations at thePM3 level, we took NC = 1500.

III. RESULTS AND DISCUSSION

A. Infinite one sided hydrogenated graphene

Figure 1 shows two side views of relaxed infinite (withperiodic boundary condition applied in both directionsof the plane) B-GO (a) and AC-GO (b) at T=10K us-ing the MD method. In the AC-GO configuration, thehydrogens are relatively far from each other and the C-H bonds are mutually parallel and perpendicular to thez = 0 plane, due to symmetry. In the B-GO the C-H bonds are attached to nearest neighbors C-C bond,which induces a corrugation in the hydrogen layer withC-H bonds that are not fully perpendicular to the z = 0plane, mainly because of the sp3 hybridization but alsodue to the stronger repulsion between te relatively closehydrogen atoms. Very similar configurations were ob-tained for GF, which are therefore not shown. It is im-portant to note that such flat GOs (and one sided GFs)are energetically unfavorable [38]. In this study we re-port on the structural transformations of these systemsinto stable, non-flat structures.

B. Ab-initio results: Graphone

In Fig. 2(a) we show the optimized configuration of B-GO using ab-initio calculations with B3LYP/6-31G* and504 atoms. Notice that the initial non-relaxed configura-

(a) ESP

(b) HOMO

(c) LUMO

FIG. 3: (Color online) Electrostatic potential (a) and theHOMO (b) and LUMO (c) for B-GO during rolling.

tion was a flat sheet. In Fig. 2(b) an example of resultsfrom our semiempirical calculation using PM6 is shown.

Figure 3(a) shows the electrostatic surface potential(ESP) of B-GO before the completion of the rolling pro-cess. The corresponding HOMO and LUMO are shown inFigs. 3(b,c) respectively. During rolling both HOMO andLUMO are localized at both ends simultaneously whichis a consequence of the equivalent geometry. The ESP ofcompletely rolled B-GO is shown in Fig. 4(a). The ESPindicates that the spiral structure has ionic characteris-tics, the red (blue) color indicating positively (negatively)charged regions, which stabilizes the spiral geometry evenmore.

Surprisingly, after complete rolling, the HOMO andthe LUMO are separated and both localized in only oneend, as can be seen from Figs. 4(b-c), whereas beforecomplete rolling they were localized in both ends simul-taneously as already mentioned before (see Figs. 3(b,c)).These effects are related to the differences in electroneg-ativity of the simulated atoms (H<C<F). Because of thedifference in ESP at the two edges, the increment of theenergy of the LUMO is larger than that of the HOMO,which results in a widening of the energy gap from 0.1 eV

4

(a) ESP

(b) HOMO (c) LUMO

FIG. 4: (Color online) (a) Electrostatic potential around spi-ral graphone and the HOMO (b) and LUMO (c) of the system.

for the flat sheet to 0.3 eV for the spiral structure. This isshown more explicitly in Fig. 5, which reveals an almostlinear increase of the gap during the evolution to a spiral.

C. Ab-initio results: One sided fluorinatedgraphene

Very similar results are found for GFs. Figure 6(a)shows the spiral GFs obtained using B3LYP/6-31G*.The spiral GF formed using the PM6 method is shownin Fig. 6(b). These configurations are minimum energyconfigurations of B-GF. Similarly as for GO, the rolling isdue to the one-sided, partial (here 50 %) coverage with Fatoms and corresponding sp3 hybridization. The rollingprocess starts from free boundaries where there is no re-sistance against any torque.

D. Classical molecular dynamics simulation results:large size flakes

Using classical simulations, we first investigated thepossibility to create hydrogenated CNT from one-sided hydrogenated AC-GO nano-ribbons, with periodicboundary condition along the zig-zag edge, having a spe-cific length equal to L=13.4 A between the two free ends

FIG. 5: (Color online) (a) HOMO-LUMO energy diagramfor four different instances of the rolling process and (b) thevariation of the energy gap during rolling (for eight steps) forthe B-GO shown in Fig. 2(left).

(a)

(b)

FIG. 6: (Color online) Spiral B-GF from DFT calculations for504 atoms (a). Spiral B-GF from semiempirical calculations(PM6) for 1428 atoms (b).

(in the flat geometry) . After relaxing the system at 10Kwe found that always a (5,5) CNT is formed independentof the dimension of the box in the periodic direction (seemovie in supplementary material [39]). The used lengthfor B-GO, i.e. L=13.4 A, agrees with the perimeter ofa one-sided hydrogenated (5,5) CNT, i.e. 5

√3a0 with

a0 ∼= 1.5A. The movie in Ref. [39] shows the time evolu-tion for the rolling of an AC-GO which eventually formsa (5,5) hydrogenated CNT. This is consistent with pre-vious results on the formation of CNT from partially hy-drogenated graphene [25]. Note however that the forma-tion of these nanotubes is constrained by the choice of

5

(a)

(b)HOMO (c) LUMO

FIG. 7: (Color online) ESP(a), HOMO (b) and LUMO (c)for the B-GF system shown in Fig. 6(left)

the length of the ribbon, which has to be relatively smalland should match with the size of an (n,n) tube.In the remainder of this section we show the rolling

effect for much longer nano-ribbons, not leading to tubeformation, using classical MD simulation. We used gra-phone nano-ribbons with free zig-zag edges and periodicboundary conditions in the direction parallel to theseedges (lateral side) and found that the final, minimal en-ergy configuration of both GO and GF is a spiral struc-ture similar to what we found with DFT. Figures 8(a,b)show two snap shots from the rolled B-GO which are freeat two longitudinal ends (here set to be zig-zag edges).Similar results are found for AC-GOs, see Figs. 8(c,d).As expected, the corrugations in B-GO are larger thanin AC-GO. Thus, unrolling B-GO costs much more en-ergy than AC-GO.Figure 9 shows the variation of the total energy per

atom as a function of the rolling process time for AC-GO, B-GO, AC-GO* and B-GO*. Clearly B-GO* is themost stable having the lowest energy. The energy gap be-tween AC-GO (AC-GO*) and B-GO (B-GO*) is about0.16 eV/atom. Furthermore it is seen that including thevdW energy term lowers slightly the energy by ∼ 0.04eV/atom due to the attractive van der Waals interac-tion. Notice that the ionic characteristic of the rolledstructure cannot be reproduced by these classical simu-lation with AIREBO. Nonetheless, the classically foundspiral structures are quite stable, which confirms thatthe main driving force for the rolling is the one-sided ab-

sorption and corresponding sp3 hybridization and not theionic characteristics found in the DFT calculations.In Fig. 10 rolled configurations of a system consisting

of two connected GO parts that are hydrogenated at op-posite sides are shown. Hydrogens at x <0 (x >0) arebonded to the upper (lower) side of the sheet. Noticethat the AC-GO and B-GO form different patterns ofrolled GO with an extra rolled part in the middle. Thishints to the interesting possibility to engineer the rolledshape of GO carefully by selectively hydrogenating partsof the initial graphene sheet.As an additional, final result of this section we present

the rolling behavior of a system with one side covered byhydrogen and the another side covered by fluor, which wecalled ‘GFH’. Recently, by using ab-initio calculations, anegative formation energy was found for this system [40].In Fig. 11 side views are shown for the rolled structureof AC-GF (a), AC-GO (b) and AC-GFH (c) after 25 psof molecular dynamics simulations (red, green and blueballs are carbon, fluor and hydrogen, respectively). In allthree cases we used the ReaxFF potential and the simu-lations were done at T=10K, as before. It is clear fromFig. 11 that AC-GO (AC-GFH) has the largest (smallest)curvature, due to the fact that when one side is coveredby hydrogen and the other side is covered by fluor, thedriven force for rolling is partially balanced, but not com-pletely as the fluor atoms are larger leading to a strongerintra-layer repulsion at the fluor side, so that the systemstill tends to roll, albeit with a much smaller curvature.

E. Temperature effects

New structures have to be tested in terms of their sta-bility against temperature. In order to study the tem-perature effects on the spiral B-GO, after obtaining it at10K (note that in principle spiral GO can also be formedat room temperature but we set T=10K in order to min-imize thermal fluctuations and to find more rapidly theground state spiral configurations) we raised the temper-ature up to 1000K. Not so surprising in view of the sig-nificant gain in binding energy of 0.1 eV/atom ( 1200 K)for AC-GO and much more for B-GO (see Fig. 9) in theirrolled states with respect to the flat configurations, thespiral GOs keep their configuration. Beyond 700K theloops start to deform slightly. However, even at 1000Kthe system is not un-zipped and the spiral configurationis conserved [39] at least within the here used MD simu-lation time of 1 ns. For T>1000K the system starts toseparate into two different loops [39]. From these simula-tions we conclude that spiral GO should be rather stableat room temperature, facilitating its possible synthesisin future experiments. Two movies are provided in thesupplementary materials [39] to show the rolling of B-GO at T=10K and to show the stability of B-GO duringthe heating process up to T=1000 K. For GFs the spiralsystem is somewhat less stable. Close to 800 K the GFsstart to un-roll and beyond this temperature they start

6

B-GO t=50 ps

t=80 ps

a)

b)

AC-GO

t=50 ps

t=80 ps

d)

c)

FIG. 8: (Color online) The rolled boat (arm-chair) like graphone nano-ribbons after t=50 ps (a,c) and 80 ps (b,d). Thesesystems are stable up to at least 1000K.

t ( ps)

E (

eV/a

tom

)

20 40 60 80 100

-5.55

-5.5

-5.45

-5.4

-5.35

-5.3

-5.25

AC-GO

B-GO

B-GO*

AC-GO*

~0.16 eV/atom

FIG. 9: (Color online) Variation of the total energy with timefor both arm-chair and boat-like graphone.

to be fractured. Notice that the C-H bonds (C-F bonds)in GOs (GFs) are stable even after unrolling, thus no hy-drogen release was observed when heating up the rolledsheets within our simulation time of 0.1 ns.

We also applied external uniaxial compression alongthe axis of the spiral structures in order to investigatethe mechanical stability of these structures, which turnedout to resists against the external pressure much betterthan graphene. Detailed mechanical properties of thesenew spiral hydrocarbons need further investigations.

a) B-GO

b) AC-GOt=80 ps

FIG. 10: (Color online) The optimized configuration of aboat-like (a) and arm-chair like (b) semi-infinite graphone.in (a) the A-lattice and in (b) the B-lattice of carbon siteswere covered by hydrogens.

IV. CONCLUSIONS

Free boat like and arm-chair like one-sided hydrogenated/fluorinated graphene (gra-phone/fluorographene) ribbons/flakes spontaneouslyroll up to form spiral configurations which should bequite stable at room temperature. The spiral structuresexhibit strong mechanical rigidity preventing themto unroll. The main driving force behind the spiralformation is the energy relaxation associated with

7

a) AC-GF

b) AC-GO

c) AC-GFH

FIG. 11: (Color online) Side view of three different spiralstructures: AC-GF (a), AC-GO(b) and AC-GFH(c)after 25 ps of relaxation from the starting flat geom-etry.

the one-sided, asymmetric orientation of sp3 bond-

ing. Further modestly stabilizing factors are the vander Waals attractive interaction between the stackedshells and (only in the DFT calculations) the ionicinteractions between the shells, which appear to bepolarized across the shell width. Boat-like hydro-genated/fluorinated graphene yields more stable, spiralsystems than arm-chair like graphone. The graphene

sheet where one side is covered by hydrogen

and the other side by fluor is unstable and it

also forms a rolled up structure, albeit with a

smaller curvature.. The highest occupied and lowestunoccupied orbital for spiral GO and GF are localized atopposite ends of the system. The energy gap increaseswhen the system evolves from the flat to the spiral shape.

Acknowledgments

We thank A. Sadeghi, M. R. Ejtehadi and J. Aminifor their useful comments. This work is supported bythe ESF EuroGRAPHENE project CONGRAN and theFlemish Science Foundation (FWO-Vl).

[1] A. K. Geim and K. S. Novoselov, Nature Mater. 6,183 (2007); A. H. Castro Neto, F. Guinea, N. M. Peres,K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81,109 (2009).

[2] D. Pacile, J. C. Meyer, C. O. Girit, and A. Zettl, Appl.Phys. Lett. 92, 133107 (2008).

[3] P. Vogt, P. D. Padova, C. Quaresima, J. Avila, E.Frantzeskakis, M. Carmen Asensio, A. Resta, B. Ealet,and G. Lay. Phys. Rev. Lett 108, 155501 (2012).

[4] G-H. Lee, Y-J. Yu, C. Lee, C. Dean, K. L. Shepard, P.Kim, and J. Hone, Appl. Phys. Lett. 99, 243114 (2011).

[5] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang,Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A.Firsov, Science 306, 666 (2004).

[6] M. H. F. Sluiter and Y. Kawazoe, Phys. Rev. B 68,085410 (2003). J. O. Sofo, A. S. Chaudhari, and G. D.Barber, Phys. Rev. B 75, 153401 (2007).

[7] R. Nair, W. Ren, R. Jalil, I. Riaz, V. Kravets, L. Britnell,P. Blake, F. Schedin, A. Mayorov, S. Yuan, M. Katsnel-son, H. Cheng, W. Strupinski, L. Bulusheva, A. Okotrub,I. Grigorieva, A. Grigorenko, K. Novoselov, and A. K.Geim, small 6, 2877-2884 (2010).

[8] M. Neek-Amal and F. M. Peeters, Phys. Rev. B 83,235437 (2011); S. Costamagna, M. Neek-Amal, J. H. Los,and F. M. Peeters, Phys. Rev. B 86, 041408 (2012).

[9] D. W. Boukhavalov, M. I. Katsnelson, and A. I. Licht-endtein, Phys. Rev. B 77, 035427 (2008).

[10] D. C. Elias, R. R. Nair,T. M. G. Mohiuddin, S. V. Mo-rozov, P. Blake, M. P. Halsall, A. C. Ferrari, D. W.Boukhvalov, M. I. Katsnelson, A. K. Geim, and K. S.Novoselov, Science 323, 610 (2009).

[11] M. Z. S. Flores, P. A. S. Autreto, S. B. Legoas, and D.S. Galvao, Nanotechnology 20, 465704 (2009).

[12] H. Sahin, C. Ataca, and S. Ciraci, Phys. Rev. B 81,205417 (2010).

[13] O. Leenaerts, H. Peelaers, A. D. Hernandez-Nieves, B.

Partoens, and F. M. Peeters, Phys. Rev. B 82, 195436(2010).

[14] A. D. Hernandez-Nieves, B. Partoens, and F. M. Peeters,Phys. Rev. B 82, 165412 (2010).

[15] Wen, X.D., L. Hand, V. Labet, T. Yang, R. Hoffmann,N.W. Ashcroft, A. Oganov, and A. Lyakhov, Proc. Natl.Acad. Sci. 108, 6833 (2011).

[16] L. Hornekaer, Z. Sljivancanin, W. Xu, R. Otero, E. Rauls,I. Stensgaard, E. Lgsgaard, B. Hammer, and F. Besen-bacher, Phys. Rev. Lett. 96, 156104 (2006).

[17] F. Dumont, F. Picaud, C. Ramseyer, C. Girardet, Y.Ferro, and A. Allouche, Phys. Rev. B 77, 233401 (2009).

[18] R. Balog, B. Jrgensen, L. Nilsson, M. Andersen, E.Rienks, M. Bianchi, M. Fanetti, E. Lgsgaard, A. Baraldi,S. Lizzit, Z. Sljivancanin, F. Besenbacher, B. Hammer,T. G. Pedersen, P. Hofmann, and L. Hornekr, NatureMater. 9, 315 (2010).

[19] Duminda K. Samarakoon and Xiao-Qian Wang, ACSNano 3, 4017 (2009).

[20] J. Zhou, Q. Wang, Q. Sun, X. C. Chen, Y. Kawazoe, andP. Jena, Nano Lett. 9, 3867 (2009).

[21] S. Lebegue, M. Klintenberg, O. Eriksson, and M. I. Kat-snelson, Phys. Rev. B 79, 245117 (2009).

[22] Konstantin N. Kudin and Gustavo E. Scuseria, and B. I.Yakobson, Phys. Rev. B 64, 235406 (2001).

[23] Ji Zang, Minghuang Huang, and Feng Liu, Phys. Rev.Lett. 98, 146102 (2007).

[24] V. V. Ivanovskaya, P. Wagner, A. Zobelli, I. Suarez-Martinez, A. Yaya, and C. P. Ewels, Carbon Nanostruc-tures, 25, 75 (2012).

[25] D. Yu, and F. Liu, Nano Lett. 7, 3046 (2007).[26] O. O. Kit, T. Tallinen, L. Mahadevan, J. Timonen, and

P. Koskinen, Phys. Rev. B 85, 085428 (2012).[27] D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R.

Lomeda, A. Dimiev, B. K. Prince, and J.M. Tour, Nature(London) 458, 872 (2009).

8

[28] L. Jiao, L. Zhang, X. Wang, G. Diankov, and H. Dai,Nature (London) 458, 877 (2009).

[29] Juan J. Vilatela and Dominik Eder, ChemSusChem 5,456 (2012).

[30] F. Alvarez-Ramrez, J. A. Toledo-Antonio, C. Angeles-Chavez, J. H. Guerrero-Abreo, and E. Lopez-Salinas, J.Phys. Chem. C 115, 11442 (2011).

[31] G. Shen, B. Liang, X. Wang, P-C. Chen, and C. Zhou,ACS Nano 5, 2155 (2011).

[32] K. Fukui, T. Yonezawa, and H. Shingu, J. Chem Phys20, 722 (1952).

[33] M. J. Frisch, et al (GAUSSIAN 1998).[34] http : //lammps.sandia.gov[35] S. J. Stuart, A. B. Tutein, and J. A. Harrison, J. Chem.

Phys 112, 6472 (2000).[36] A. C. T. van Duin, S. Dasgupta, F. Lorant, and W. A.

Goddard, J. Phy. Chem. A 105, 9396 (2001).[37] D. W. Brenner, O. A. Shenderova, J. A. Harrison, S.

J. Stuart, B. Ni, and S. B. Sinnot, J. Phys.: Condens.Matter 14, 783 (2002).

[38] Z. Slijvancanin, R. Balog, and L. Hornekær, Chem. Phys.Lett 541, 70 (2012).

[39] Four movies of the rolled GO, GF, an the temperatureeffect and the formation of CNT are provided in the Sup-plementary Material.

[40] M. Klintenberg, S. Lebegue, M. I. Katsnelson, and O.Eriksson, Phys. Rev. B 81, 085433 (2010).